The Nehari manifold for a ψ-Hilfer fractional p-Laplacian

Abstract

In this paper, we discuss the existence and non-existence of weak solutions to the non-linear problem with a fractional p-Laplacian introduced by the ψ-Hilfer fractional operator, by combining the technique of Nehari manifolds and fibering maps. Also, we obtain some results on the ψ-Hilfer fractional operator and the Nehari manifold via the Euler functional.

Keywords:

• Fractional p-Laplacian
• existence and nonexistence of weak solutions
• Nehari manifold
• fibering maps

Mathematics Subject Classifications (2010):

• 26A33
• 35R11
• 35A15
• 35J66

Acknowledgments

The work is supported by the Fundamental Research Funds for Central Universities (2019B44914) and China Scholarship Council (201906710004). J. V. C. S. acknowledges the financial support of a PNPD-CAPES (number of process $n^0$88882.305834/2018-01) scholarship of the Postgraduate Program in Applied Mathematics of IMECC-Unicamp. All authors' contributions to this manuscript are the same. All authors read and approved the final manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The work is supported by the Fundamental Research Funds for Central Universities [grant number 2019B44914] and China Scholarship Council [grant number 201906710004]. J. V. C. S. acknowledges the financial support of a (number of process $n^0$) scholarship of the Postgraduate Program in Applied Mathematics of IMECC-Unicamp.